1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
makvit [3.9K]
2 years ago
6

Help please! how do I calculate the coordinates of point a so that at is an altitude?

Mathematics
1 answer:
vodomira [7]2 years ago
6 0

Part (a)

Since we want segment AT to be an altitude, this means that point A is somewhere on segment RI such that angle TAI is 90 degrees. In other words, segments AT and RI are perpendicular. Check out the diagram below.

We'll need to find the slope of line RI, so we'll need the slope formula

R = (x1,y1) = (-2,-2)

I = (x2,y2) = (4,1)

m = slope of line RI

m = (y2-y1)/(x2-x1)

m = (1-(-2))/(4-(-2))

m = (1+2)/(4+2)

m = 3/6

m = 1/2

m = 0.5

The slope of line RI is 1/2 or 0.5

Now let's use point R(-2,-2) along with that slope we just found to find the equation of line RI.

Turn to point slope form

y - y1 = m(x - x1)

y - (-2) = 0.5(x -(-2))

y + 2 = 0.5(x + 2)

y + 2 = 0.5x + 1

y = 0.5x + 1 - 2

y = 0.5x - 1

This is the equation of line RI. We'll use it later.

----------

We found that the slope of line RI was 1/2.

The negative reciprocal involves us flipping the fraction and flipping the sign to get -2/1 or simply -2.

The perpendicular slope is -2. This is the slope of altitude AT.

We want line AT to go through T(-2,4), so we'll use this point along with the perpendicular slope we just found to calculate the equation of line AT.

We'll turn to the point slope form

y - y1 = m(x - x1)

y - 4 = -2(x - (-2))

y - 4 = -2(x + 2)

y - 4 = -2x - 4

y = -2x - 4 + 4

y = -2x

The equation of the line that goes through points A and T is y = -2x.

----------

To summarize so far, we have these two equations

  • y = 0.5x - 1 .... equation of line RI
  • y = -2x .... equation of line AT

Apply substitution to solve for (x,y) to find the intersection point. This will determine where point A is located.

y = 0.5x - 1

-2x = 0.5x - 1

-2x-0.5x = -1

-2.5x = -1

x = -1/(-2.5)

x = 0.4

Then we can determine y like so

y = -2x

y = -2(0.4)

y = -0.8

Therefore, point A is located at (0.4, -0.8). Both coordinate values are exact. In fraction form, we can say that the point is (2/5, -4/5), but I find decimals easier to work with in this instance.

<h3>Answer:  (0.4, -0.8)</h3>

===============================================================

Part (b)

To find the length of segment AT, we can find the distance from A to T. As you can probably guess, we'll use the distance formula.

A = (x1,y1) = (0.4, -0.8) ... found back in part (a)

T = (x2,y2) = (-2, 4) ... given

d = \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 - (-0.8))^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 + 0.8)^2 }\\\\d = \sqrt{ (-2.4)^2+(4.8)^2 }\\\\d = \sqrt{ 5.76+23.04 }\\\\d = \sqrt{ 28.8 }\\\\d \approx 5.36656\\\\d \approx 5.37\\\\

The distance from point A to point T is approximately 5.37 units. This means that segment AT is roughly 5.37 units long.

<h3>Answer: 5.37 units</h3>

You might be interested in
Percy use hose to wash pig sty for 11 minutes. The hose uses 7 liters of water every minute how many liters did percy pig use to
kykrilka [37]

Answer:

Percy used 77 liters to wash

Step-by-step explanation:

This question can be solved using a rule of three.

Each minute of washing costs 7 liters.

She washed for 11 minutes.

So

1 minute - 7 liters

11 minutes - x liters

x = 7*11 = 77

Percy used 77 liters to wash

6 0
3 years ago
Please help me!! I don’t get this!
atroni [7]

Answer:

2. d) (x-1)²+(y+5)²=128

3.c) (x-3)²+(y+2)²=841

Step-by-step explanation:

5 0
3 years ago
Maria and Jason are saving gas money for their trip to Boston. Maria has saved $20 more than double what Jason has. Combined Mar
valentina_108 [34]

Answer:

$60

Step-by-step explanation:

Jason saved gas money (x).  Maria saved $20 more than double what Jason has (20 + 2x).  Combined, they saved $200.  Solve for x for Jason's amount.

(x) + (20 + 2x) = 200

x + 20 + 2x = 200

3x + 20 = 200

3x + 20 = 200

3x + 20 - 20 = 200 - 20

3x = 180

3x/3 = 180/3

x = 60

Jason saved $60 for this trip.

3 0
3 years ago
Explanation?<br> please help asap
elena-s [515]

Answer:

70 degrees = a

Step-by-step explanation:

Triangle= 180 degrees.

Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees

4 0
2 years ago
What expression is equivalent to 12x⁴ over 4x¹⁶
alexgriva [62]

Answer:

\frac{3}{x^1^2}

Step-by-step explanation:

\frac{12x^4}{4x^1^6}=3x^4/x^16

bring "x^4" to the bottom to subtract it with x^16

3/x^16*x^-4

3/x^12

hope this helps!

7 0
3 years ago
Other questions:
  • For what values of x is the x^2+2x=24 true?
    5·1 answer
  • What is a googol multiplied by 100? How many zeros will it have?
    14·1 answer
  • Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by
    14·1 answer
  • How can the Pythagorean theorem be used to help classify triangles
    9·1 answer
  • You earn a 12% commission for every car you sell. How much is your commission if you sell a $23,000 car?
    14·1 answer
  • if a line is perpendicular to each of two intersecting lines at their point of intersection then what is the line
    5·1 answer
  • Just tell me how ur day was C:
    6·2 answers
  • How do u friend someone on brainlest and whaat is 1 +1 help never leaned how to count bc im number 1
    12·2 answers
  • 2. 47 in = ? ft ? in<br> a .3ft 11in<br> b. 3ft 9in<br> c. 4ft 0in<br> 564 ft 0 in
    10·1 answer
  • Given f(x) = 3x − 4 and g(x) = f(2x), which table represents g(x)?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!